Friday, March 9, 2012

An account of laws

According to the Lewisian best system analysis of laws, a proposition p is a fundamental law if and only if it is an axiom in the best system. There is room for variation in the concept of a best system, but a standard version in deterministic settings is that the best system comprises only truths and optimizes the brevity of its axioms and the informativeness of its theorems about the world. The biggest problem for me with the best system account is that the fact that something is an axiom in the best system simply does not make it be explanatory.

I think this is a better account. A proposition p is a fundamental law of nature provided that:

p is an axiom in the best system, and

God wills p, as such.

(I am not sure if the will in (2) should be taken to be antecedent or consequent. If miracles are counterinstances to laws, it must be antecedent. But a lot of people think that's a bad account of miracles, and that allows it to be consequent.)

The "as such" in (2) rules out a case where God instead of willing p, wills something that entails p.

This account solves the explanatory problem with Lewis's account by making the fundamental laws be explanatory. They are not explanatory directly because they are axioms in the best system, but rather because God wills them.

Interestingly, I think (1) may imply (2) in the actual world, by divine omnirationality. For that p has the kind of simplicity and fecundity that axioms in the best system are going to have gives God a reason to will p. And since p in fact holds, presumably God willed p. The only exception is going to be if p reports the sort of thing that God has reason to distance himself from. Suppose, for instance, that everyone who is tempted a certain way sins. Then that universal generalization might be a best system axiom, but God has reason not to will it. But in fact it does not seem that any axioms in our world's best system are going to be like that—such regularities don't seem to be far-reaching enough. All the candidates we hear about from physics are propositions that God does not seem to have reason to distance his will from.

If this is right, then in the actual world, all the axioms in the best system are fundamental laws, and Lewis is contingently right. Moreover, this line of thought shows that the fact that p is an axiom in the best system makes it likely that God wills it. Consequently, as long as we know that God exists, we get to keep the epistemological benefits of Lewis's system.

The antecedent/consequent will is found in Aquinas, and I think also in reformed thinkers. The locus classicus is that Scripture tells us both that God wants all to be saved and yet it tells us that God sentences "many" to damnation. So, one distinguishes between God's antecedent will and his consequent will. It is only God's consequent will that is efficacious. With his antecedent will, God wills things that may only be ceteris paribus principles. Thus God antecedently wills all to be saved, and also antecedently wills all the wicked who reject Christ to be damned. Consequently, if x is one of the wicked who in the end rejects Christ, God consequently and efficaciously wills that x be damned.

Another place where the distinction might be found is when we say that God wants people not to sin. That's a matter of antecedent will. If it were a matter of consequent will, then nobody would sin.

As for occasionalism, I am a causal particularist, and I take causation not to reduce to laws. There may, however, be causal laws--laws that say that in conditions C, A causes B. And if C obtains, then that explains why A causes B. But the explanation is not constitutive. It is not the case that what constitutes A's causing B is condition C plus the law. (People inclined to a legal positivism about marriage will say that when the law says that in conditions C, A is married to B, then A's being married to B is constituted by C and the law. But I deny this: marriage is a status whose truth grounds are over and beyond the decrees of the law. And similarly for causation.)

I wish to understand how Lewis's view relates to the Principle of Sufficient Reason. First, can a Lewisian possible world be a brute fact?

Suppose I imagine two possible worlds, and I think of a contingent fact as a temporal slice or moment of a world. Suppose the first world has no brute facts in it and every temporal slice is causally related to its predecessor. Thus this world looks like the way a typical scientists views evolution: things change with respect to time as described by laws of physics. However, I am assuming for argument purposes that violations of the PSR are possible; there just don't happen to be any in world one.

Imagine the second world looks exactly like the first. Except now every temporal slice is a brute fact.

Now, you have said that a brute fact has no objective probability associated with it. I assume this applies to a collection of brute facts as well. On a non-Lewisian view, it seems to me that there just is no fact of the matter as to whether world 1 is more likely than world 2. Is that incorrect?

But on a Lewisian view, it would seem that a hypothetical meta-observer who can see all the possible worlds would be able to observe the frequency of one world type with respect to another. If so, does that imply that Lewisian possible worlds can't be brute facts because there shouldn't be a fact-of-the-matter regarding relative likelihood?

For Lewis, there is no difference between the two worlds you've described. According to Lewis: Causal facts supervene on counterfactual facts. Counterfactual facts supervene on laws and the arrangement and properties of matter. Laws supervene on the arrangement and properties of matter. So as long as the arrangement and properties of matter are the same, so are the laws, the counterfactual facts and the causal facts.

This is meant to be a deflationary account of law, perhaps as a way of answering questions left unanswered by an Aristotelian metaphysics of causation.

Suppose God creates an infinite sequence of coins (they don't have to be simultaneous), laid out somewhere. If the coins are all heads up, or all tails up, or if they alternate, or if they have some other finitely describable pattern (in a language whose terms correspond to perfectly natural kinds and entities), that's a law. But most arrangements of infinitely many coins will not be nomic.

Could God will one of the "messy arrangements" to be a law? Well, yes, but not in an otherwise simple universe. Imagine a world where the arrangement of the countably infinitely many coins allows you to predict some incredibly states of affairs involving larger cardinalities. Then the messy arrangement might get to be a law.

This may be a dead post, but here goes! Although very attractive what I don't understand about your baptism of Lewis's best-system approach is how God's standards of explanatory simplicity and strength could ever even approximate to our own. Isn't explanatory power relative to the goals of the particular scientific inquiry we're engaged with? Indeed I understand that recent developments of BSA turn its psychologistic vices into pragmatist virtues in roughly this way: on this view, the spectre of relativism in establishing optimal combinability of strength + simplicity is to be *welcomed*, since scientists will want and expect the assessment to vary across different areas of empirical inquiry. Now God might have good reasons to equip us with epistemic access to best-systems conducive to us, but what need could there be for a divine best-system if God is omniscient anyway?

It's not so much God's standards of explanatory simplicity, but God's aesthetic standards. This works best with physics: the best physics is really beautiful, the physicists say (I remember experiencing this beauty when reading Dirac's PQM long ago--the mathematical details have gone out of my mind by and large, but the memory of beauty remains). But I think there can be a beauty in theories in the special sciences as well.

Certainly, the standards differ between the sciences. I think that's because God's work of art is multimodal. In a multimodal work of art, such as a musical, there will be different, though interrelated, aesthetic standards operating for different parts of the work: the music, the dancing, the acting and the scenery are all evaluated by different standards.

I think what happened in the scientific revolution is that we got a feel for the basic genre of God's work at the lower levels (physics and chemistry, say)--a very mathematical and elegant genre. A genre brings along with it a special set of aesthetic standards. (This isn't relativism. It need not, for instance, be true that for every set of aesthetic standards there is a genre that implements these standards.)

And as we have made progress in the special sciences, we have come to a better grasp of the genre of God's work with respect to other modes--the biological, the geological, the astronomical, etc.

So I see God's reasons here as two-fold: he has aesthetic reasons for creating instances of simplicity and elegance (Leibniz is big on this, though he doesn't always use aesthetic vocabulary) and he has reasons given his interrelated decision to make beings whose empirical reasoning proceeds in the way ours does.

God's aesthetic standards are always objectively correct (though they may be genre relative--he could have created a beautiful world governed by other genres), and he made us capable of recognizing the standards of these genres. This recognitional ability makes us capable of prediction and theorization, much as knowing the genre of a film can help you defeasibly predict facts about what is coming (especially negative ones, such as that there will not be ghosts) and understand the purposes behind the work.

Thank you Alex for an amazingly rapid and full response. I think I get it now - had I read your chocolates-in-gold-boxes scenario more carefully I might have got it quicker (chocolates + gold go nicely together).

Could I press you on a related issue? I was a bit surprised to see you adopt a Lewis-plus-theism take on laws. Reading your recent book last week I just assumed (though not sure if you state this explicitly?) that your Aristotle-plus-Leibniz metaphysic would sit most naturally alongside with a capacities account of laws - i.e. you either reduce laws to law-statements about substantial capacities (or dynamic properties?) or else eliminate them completely in favour of the latter.

This metaphysic delivers the modal goods w/o positing puzzling governing entities that are extrinsic to their governed objects - so it's a neat via media b/w Armstrong and Lewis etc. (tho' am undecided over your bold attempt to marshall this into an argument for God, but at the very least you end up with a pretty plausible account that seems way too rich ontologically for the naturalist's digestive system).

But hence the puzzlement: why hold onto the Lewis-plus-theism view? How come this doesn't just overdetermine/confuse the issues? Or is that view just a kind of add-on theory about our epistemic access to - and the cognitively-pleasing features of - a best-system once we've done an optimality assessment of all the capacities that underpin law statements etc.

First of all, this post is very speculative, and my level of commitment to this Lewis+theism view is low.

But I guess I've come to be open to the idea that capacities aren't enough to yield all the laws scientists think of as laws.

Take, for instance, conservation of energy. Say that an entity is a conserver provided that it lacks a capacity to create or destroy energy. Then:

1. All actual physical things conservers.

But why is (1) a law?

Compare (1) to another claim about capacities:

2. All actual physical things are nurs,

where a nur is an entity that lacks the capacity of having a unicorn as a descendant.

Now (1) may be a law, but (2) is not, just as it's not a law that there are no unicorns. After all, unicorns might evolve, and if they do that won't violate any law. But if unicorns evolve, they will be non-nurs.

But the concept of a conserver and the concept of a nur are defined in a rather parallel way in terms of capacities.

So capacities aren't sufficient to give us a distinction between accidental generalizations like 2 and non-accidental generalizations like 1.

Maybe we could say: But non-nurs are causally possible, while non-conservers aren't. However, imagine a deterministic world where non-nurs can't evolve because the initial conditions are compatible with unicorns. It still wouldn't be a law that all physical things are nurs, because the initial conditions aren't a matter of law.

One move would be simply to abandon the notion of a law. Anything we need the concept of a law for can be done by invoking facts like 1 or 2 about the distribution of capacities among the existent things. I am open to that move. But I am also open to salvaging the concept of a law.

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